The sensitive and reliable detection of exosomes is crucial for the early diagnosis and prognosis of various diseases. This work presents a label-free surface plasmon resonance (SPR) aptasensor based on two-dimensional (2D) ultrathin cobalt boride nanosheets embedded with aptamer-templated silver nanoclusters (Apt/AgNCs@CoB) for the sensitive detection of the exosomal marker CD63. The Apt/AgNCs@CoB Schottky junction exhibited a high light absorption, which enhanced the coupling with SPR and promoted the electric field at the interface. This heterojunction facilitated strong charge transfer at the SPR sensing interface and amplified the SPR signal due to the localized SPR of the silver nanoclusters. Furthermore, the integration of aptamer strands in the Apt/AgNCs@CoB nanohybrid ensured the stable anchorage of probe molecules and high affinity for the target analyte. This integration simplified the aptasensor construction through a one-step modification of the SPR gold chip, which led to the improved sensitivity and direct detection of CD63. The proposed SPR aptasensor achieved an ultralow detection limit of 0.15 fg mL